Sigma-delta modulation has become the preferred method for performing high resolution analog to digital (A/D) conversion on narrowband signals. Traditional low pass sigma-delta modulation techniques have been extended to bandpass A/D converters ideally suited for converting the narrowband Intermediate Frequencies (IF) found in wireless systems. Such narrowband A/D converters are particularly well suited to superheterodyne radio architecture. The resolution obtainable in such bandpass A/D converters is dependent on several factors including the method of implementing the transmission zeroes in the noise transfer function. Analog to digital converters based on known single bit type sigma delta modulators are inherently linear but the accompanying quantization noise is only small for low frequencies and undesirably high at higher signal frequencies. The high and low frequencies are relative to the sampling clock frequency.
Certain circuit designs for performing bandpass sigma-delta modulation have used switched capacitor techniques that depend on ratio matching of the capacitors to place the transmission zeros at a quarter of the sampling rate (f.sub.s /4). This is desirable, since simple resonator circuit implementations are possible when operating bandpass modulators at f.sub.s /4. Some switched capacitor techniques, however, have shown degraded performance due to capacitor mismatch effects. Bandpass sigma-delta modulators implemented with switched capacitor technology require a capacitor ratio tolerance on the order of the ratio of the desired signal bandwidth to the frequency of the signal being converted. For moderately narrowband signals this requirement has proved to be barely tolerable and, for extremely narrowband signals this requirement has been too stringent.
Several articles exist in the prior art which relate bandpass sigma-delta modulation techniques. For example, an article entitled "Multibit Bandpass Delta-Sigma Modulators Using N-path Structures", by Schreir and B. R. Hong et al., IEEE International Symposium on Circuits & Systems, 1992, discloses the use of multibit quantization to overcome the quantization noise power problems associated with single bit sigma-delta modulators. An article entitled "A 15b 30 kHz Bandpass Sigma-Delta Modulator", by L. Longo et al., IEEE International Solid-State Circuits Conference, 1993, discloses the use of bandpass filters with infinite Q's as opposed to integrators used in lowpass modulators. An article entitled "Multistage Bandpass Delta Sigma Modulators", by Ribner, IEEE Transactions on Circuits and Systems, 1994, discloses an architecture for oversampled delta sigma A/D converters.
These articles, in part, disclose methods and circuits for implementing bandpass sigma delta based analog to digital conversions which rely on high order transfer functions realized by integrator based and/or unity gain delay circuits. However, the performance of these integrator based circuits are limited by design complexity, capacitor component mismatching, finite operational amplifier gain and bandwidth. Accordingly, there is a need to provide a circuit for implementing transmission zeros optimally in sigma delta based analog to digital conversion of narrowband signals.